Place cubed potatoes in a pot of salted water, bring to a boil, and cook for 15-20 minutes until tender; drain and mash with 2 tbsp butter and 1/2 cup milk.
In a small saucepan, combine carrots, 1/4 cup water, 1 tbsp butter, and honey; simmer covered for 10 minutes, then uncover and cook until liquid reduces to a glaze.
Season chicken breasts with salt, pepper, thyme, and rosemary; heat olive oil in a skillet over medium-high heat and sear chicken for 6-8 minutes per side until internal temperature reaches 165F.
Remove chicken from skillet and set aside; melt remaining 1 tbsp butter in the same skillet and whisk in flour to create a roux.
Gradually whisk in chicken stock to the roux and simmer until thickened; stir in fresh parsley.
Plate the mashed potatoes and carrots, then top the chicken with the prepared herb gravy.